BAGHDAD - The Iraqi government appealed to U.S. Defense Secretary Chuck Hagel on Tuesday for additional air power and heavy weapons as Iraq struggles to expel the well-armed Islamic State militants who are dug in across a vast area of the country.

Hagel, paying an hours-long visit to Iraq as he prepares to step down from his Pentagon position, underscored the significant expansion in U.S. military assistance since the Islamic State group swept into northern Iraq from Syria in the summer. But he also delivered the tough-love message of President Obama's White House: The fight is ultimately Iraqis' own to win or lose.

"As Iraqi leaders and the people of Iraq know, only they can bring lasting peace to their country," Hagel told reporters after meetings with senior Iraqi officials. "I believe the Iraqi people are resolved to do this."

Hagel said he was "encouraged" by the progress that Iraq was making six months after the fall of Mosul, the country's second-largest city, as Iraqi forces claim some successes in dislodging the militant group from areas such as the Mosul dam or around the critical Baiji oil refinery.

Prime Minister Haider al-Abadi, who U.S. officials are hoping will be able to end the sectarian feuds that provided a foothold for the Islamic State, said the extremist group was now "on the descent" despite its extensive arsenal and its ability to move back and forth between Iraq and Syria.

"We are very thankful for the support that's been given to us," Abadi told Hagel at the start of a meeting in Baghdad's fortified Green Zone. Since the summer, Obama has sent 1,650 U.S. troops to Iraq. As part of a plan to retrain portions of the Iraqi army, that force could grow to about 3,000 in the short term.

Abadi stressed the urgency of defeating the Islamic State. "Our forces are very much advancing on the ground. But they need more air power and more . . . heavy weaponry. We need that," he said.

Speaking to reporters later, Hagel declined to say whether the United States would increase the tempo of airstrikes that its warplanes, along with those from allied nations, have been conducting on militant targets in Iraq since August.